Chemical potential in disordered organic materials

Charge carrier mobility in disordered organic materials is being actively studied, motivated by several applications such as organic light emitting diodes and organic field-effect transistors. It is known that the mobility in disordered organic materials depends on the chemical potential which in turn depends on the carrier concentration. However, the functional dependence of chemical potential on the carrier concentration is not known. In this study, we focus on the chemical potential in organic materials with Gaussian disorder. We identify three cases of non-degenerate, degenerate and saturated regimes. In each regime we calculate analytically the chemical potential as a function of the carrier concentration and the energetic disorder from the first principles.Comment: 5 pages, 3 figure

Elastic response of filamentous networks with compliant crosslinks

Experiments have shown that elasticity of disordered filamentous networks with compliant crosslinks is very different from networks with rigid crosslinks. Here, we model and analyze filamentous networks as a collection of randomly oriented rigid filaments connected to each other by flexible crosslinks that are modeled as worm-like chains. For relatively large extensions we allow for enthalpic stretching of crosslinks' backbones. We show that for sufficiently high crosslink density, the network linear elastic response is affine on the scale of the filaments' length. The nonlinear regime can become highly nonaffine and is characterized by a divergence of the elastic modulus at finite strain. In contrast to the prior predictions, we do not find an asymptotic regime in which the differential elastic modulus scales linearly with the stress, although an approximate linear dependence can be seen in a transition from entropic to enthalpic regimes. We discuss our results in light of the recent experiments.Comment: 10 pages, 11 figure

Active biopolymer networks generate scale-free but euclidean clusters

We report analytical and numerical modelling of active elastic networks, motivated by experiments on crosslinked actin networks contracted by myosin motors. Within a broad range of parameters, the motor-driven collapse of active elastic networks leads to a critical state. We show that this state is qualitatively different from that of the random percolation model. Intriguingly, it possesses both euclidean and scale-free structure with Fisher exponent smaller than $2$. Remarkably, an indistinguishable Fisher exponent and the same euclidean structure is obtained at the critical point of the random percolation model after absorbing all enclaves into their surrounding clusters. We propose that in the experiment the enclaves are absorbed due to steric interactions of network elements. We model the network collapse, taking into account the steric interactions. The model shows how the system robustly drives itself towards the critical point of the random percolation model with absorbed enclaves, in agreement with the experiment.Comment: 6 pages, 7 figure

Actively stressed marginal networks

We study the effects of motor-generated stresses in disordered three dimensional fiber networks using a combination of a mean-field, effective medium theory, scaling analysis and a computational model. We find that motor activity controls the elasticity in an anomalous fashion close to the point of marginal stability by coupling to critical network fluctuations. We also show that motor stresses can stabilize initially floppy networks, extending the range of critical behavior to a broad regime of network connectivities below the marginal point. Away from this regime, or at high stress, motors give rise to a linear increase in stiffness with stress. Finally, we demonstrate that our results are captured by a simple, constitutive scaling relation highlighting the important role of non-affine strain fluctuations as a susceptibility to motor stress.Comment: 8 pages, 4 figure

How the DNA sequence affects the Hill curve of transcriptional response

The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here we analyze existing experimental data and demonstrate that the Hill coefficient characterizing the binding of transcription factors to their cognate sites can in fact be larger than one -- the standard indication of cooperativity -- even in the absence of any standard cooperative binding mechanism. By studying the problem analytically, we demonstrate that this effect occurs due to the disordered binding energy of the transcription factor to the DNA molecule and the steric interactions between the different copies of the transcription factor. We show that the enhanced Hill coefficient implies a significant reduction in the number of copies of the transcription factors which is needed to occupy a cognate site and, in many cases, can explain existing estimates for numbers of the transcription factors in cells. The mechanism is general and should be applicable to other biological recognition processes.Comment: 9 pages, 7 figure

Classes of fast and specific search mechanisms for proteins on DNA

Problems of search and recognition appear over different scales in biological systems. In this review we focus on the challenges posed by interactions between proteins, in particular transcription factors, and DNA and possible mechanisms which allow for a fast and selective target location. Initially we argue that DNA-binding proteins can be classified, broadly, into three distinct classes which we illustrate using experimental data. Each class calls for a different search process and we discuss the possible application of different search mechanisms proposed over the years to each class. The main thrust of this review is a new mechanism which is based on barrier discrimination. We introduce the model and analyze in detail its consequences. It is shown that this mechanism applies to all classes of transcription factors and can lead to a fast and specific search. Moreover, it is shown that the mechanism has interesting transient features which allow for stability at the target despite rapid binding and unbinding of the transcription factor from the target.Comment: 65 pages, 23 figure